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Fundamental of Quantum Mechanics... Diffraction of Light/Electron by One Slit... Double-slits Experiments for Electrons... Wave-Particle DualityA beam of light can be thought as ...... de

Fundamental of Quantum Mechanics

Quantum Mechanics

Diffraction of Light/Electron by One Slit

Double-slits Experiments for Electrons

Wave-Particle Duality

A beam of light can be thought as

Electric Field

Direction of propagation

Wavelength λ (Newton/Planck/Einstein) (Huygens/Maxwell/Hertz)

Zero mass, speed: c = 3 x 108 m/s

Energy carried by each particle:

h = 6.6262 x 10-34 J.s (Planck)

ν (frequency) = 1/T (period)

Particle (Photon):

- Photoelectric Effect

Wave (Electromagnetism):

- Interference

c = λν

Dispersion relation (Free space)

de Broglie’s Hypothesis

“ Light can behave like a particle and Matter/Electron

can behaves like a wave

It turns out that everything’s kind of mixed together at the fundamental microscopic scale

= h p

E = pc

E = h⌫

Energy of Photon by Special Relativity:

Energy of Photon by Planck’s theory:

de Broglie’s wavelength:

Wave if λ << scale Particle if λ >> Scale

For a Non-relativistic Free Particle

Momentum is p = mv, here is v is the speed of the particle

Bullet: m = 0.1 kg; v = 1000 m/s

Total energy of a free particle, E, is kinetic energy:

p =

h

mv =

h p 2mE

E = K = p

2

2m =

mv2 2

What is the de Broglie’s wavelength of an electron moving at 2.2 x 106 m/s

What is the de Broglie’s Wavelength of an Electron?